| Issue |
ESAIM: COCV
Volume 6, 2001
|
|
|---|---|---|
| Page(s) | 539 - 552 | |
| DOI | https://doi.org/10.1051/cocv:2001100 | |
| Published online | 15 August 2002 | |
Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria
1
Depto. Ingeniería Matemática, Universidad de Chile, Casilla 170/3, Correo 3,
Santiago, Chile; falvarez@dim.uchile.cl.
2
Centro de Modelamiento Matemático (CNRS UMR 2071),
Universidad de Chile, Blanco Encalada 2120, Santiago, Chile.
3
Laboratoire ACSIOM-CNRS FRE 2311,
Département de Mathématiques, Université de Montpellier II, Place Eugène Bataillon, 34095 Montpellier Cedex 05,
France; attouch@math.univ-montp2.fr.
Received:
1
June
2000
Revised:
3
April
2001
It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically vanishing restoring force into the evolution equation.
Mathematics Subject Classification: 34E10 / 34G05 / 35B40 / 35L70 / 58D25
Key words: Second-order in time equation / linear damping / dissipative hyperbolic equation / weak solution / asymptotic behavior / stabilization / weak convergence / Hilbert space.
© EDP Sciences, SMAI, 2001
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